Your dog eats grass. Does he lack vegetables, or vitamins? If not, why does he do it?
The grass eating is purely and simply the dog's method of making himself sick and relieving some indisposition of the digestion. Bilious dogs do it to get rid of the excessive bile built up in the stomach and, after being sick, will very often feel quite all right and be ready for a meal.
Some dogs left to wander in the countryside eat all sorts of greenstuffs, which is taken to mean that they lack vegetables in their diet. A dog properly fed does not indulge in this habit.